Related papers: Annihilating polynomials for quadratic forms and S…

We extend Kostant's result on annihilator ideals of non-singular simple Whittaker modules over Lie algebras to (possibly singular) simple Whittaker modules over Lie superalgebras. We describe these annihilator ideals in terms of certain…

We provide a micro-local necessary condition for distinction of admissible representations of real reductive groups in the context of spherical pairs. Let $\bf G$ be a complex algebraic reductive group, and $\bf H\subset G$ be a spherical…

Let $R = k[x_1, \dotsc , x_n]$ denote the standard graded polynomial ring over a field $k$. We study certain classes of equigenerated monomial ideals with the property that the so-called complementary ideal has no linear relations on the…

Suppose $I$ is an ideal of a polynomial ring over a field, $I\subseteq k[x_1,\ldots,x_n]$, and whenever $fg\in I$ with degree $\leq b$, then either $f\in I$ or $g\in I$. When $b$ is sufficiently large, it follows that $I$ is prime.…

H. J. S. Smith proved Fermat's two-square theorem using the notion of palindromic continuants. In this paper we extend Smith's approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of…

Necessary conditions for various algebraic types of the Weyl tensor are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically…

We prove that in every ring of generalised power series with non-positive real exponents and coefficients in a field of characteristic zero, every series admits a factorisation into finitely many irreducibles of infinite support, the number…

Let $L/K$ be a Galois extension of number fields with Galois group $G$. We discuss a new method to obtain elements in $\mathbb{Z}[G]$ which annihilate the class group of $L$. Using this method, we obtain annihilators of class groups of…

Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$ and $I$ is an ideal in $A$. Then M. P. Murthy conjectured that $\mu(I)=\mu(I/I^2)$, where $\mu$ denotes the minimal number of generators. Recently, Fasel \cite{F}…

We determine simplicity criteria in characteristics 0 and $p$ for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal…

We consider vanishing of Ext and Tor, especially over Artinian rings. In particular, we prove the Auslander-Reiten conjecture for all commutative local rings in which the cube of the maximal ideal is zero.

We present an alternative account of the problem of classifying and finding normal forms for arbitrary bilinear forms. Beginning from basic results developed by Riehm, our solution to this problem hinges on the classification of…

We consider the question when the so--called spectral condition} for Hermite subdivision schemes extends to spaces generated by polynomials and exponential functions. The main tool are convolution operators that annihilate the space in…

Let $L$ be the language of rings. We provide an axiomatization of the $L$-theories of quaternions and octonions and characterize their models: they coincide, up to isomorphism, with quaternion and octonion algebras over a real closed field,…

In this article, we propose a few sufficient conditions on polynomials having integer coefficients all of whose zeros lie outside a closed disc centered at the origin in the complex plane and deduce the irreducibility over the ring of…

We give necessary conditions satisfied by the set of odd prime divisors of binary perfect polynomials. This allows us to get a new characterization of all the known perfect binary polynomials.

We investigate the higher divisorial ideal $D(I):= Ann(Ext^g_R(R/I,R))$ associated to an ideal I of grade g. Our main focus is the containment problem $D(I) \subseteq \overline{I}$. We show that this inclusion holds for broad classes of…

We show that every modular form on $\Gamma_0(2^n)$ ($n\geq2$) can be expressed as a sum of eta-quotients. Furthermore, we construct a primitive generator of the ring class field of the order of conductor $4N$ ($N\geq1$) in an imaginary…

We show how several results about p-adic lattices generalize easily to lattices over valuation ring of arbitrary rank having only the Henselian property for quadratic polynomial. If 2 is invertible we obtain the uniqueness of the Jordan…

For an abelian number field K containing a primitive p-th root of unity (p an odd prime) and satisfying certain technical conditions, we parametrize the Z_p[G(K/Q)]-annihilators of the "minus" part A_K^- of the p-class group by means of…